An Islamic civil liberties group in the United States called Monday for former neurosurgeon Ben Carson, one of the leading Republican presidential candidates, to quit the contest for the party's 2016 presidential nomination after he said he would not support a Muslim for U.S. president.

Nihad Awad, executive director of the Council on American-Islamic Relations, said that Carson, a devout Christian who has been among the leaders in surveys of Republican voters, should withdraw "because he's unfit to lead, because his views are in contradiction with the United States Constitution."

Awad noted that the Constitution says that "no religious test shall ever be required as a qualification" for public office in the U.S.

"This cannot be misunderstood ... This is a very clear language to all Americans, to all generations, irrespective of who they are," Awad said at a news conference.

Carson told NBC's Meet the Press on Sunday, ''I would not advocate that we put a Muslim in charge of this nation. I absolutely would not agree with that.''

He said a president's faith should matter to voters and he described the Islamic faith as inconsistent with the Constitution, although he did not specify in which way Islam ran counter constitutional principles.

Carson's comments came amid lingering fallout over Republican Donald Trump's refusal last week to take issue with a man who, during a New Hampshire campaign event, wrongly called President Barack Obama a Muslim and said Muslims are "a problem in this country."

Carson had been running second to Trump in U.S. surveys of Republican voter sentiment for more than four months ahead of the first voting in the Republican presidential nominating contest.

But Carson slipped to third in one survey following last week's Republican presidential candidate debate, with Trump still first, but losing ground, followed by another political outsider, former technology executive Carly Fiorina. She moved to second after a strong performance at the debate.